Homoclinic intersections for geodesic flows on convex spheres

Zhihong Xia, Pengfei Zhang

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this paper, we study some generic properties of the geodesic flows on a convex sphere. We prove that, Cr generically (2 ≤ r ≤ ∞), every hyperbolic closed geodesic on S2 admits some transverse homoclinic intersections.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages221-238
Number of pages18
DOIs
StatePublished - Jan 1 2017

Publication series

NameContemporary Mathematics
Volume698
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Keywords

  • Closed geodesic
  • Convex spheres
  • Elliptic geodesic
  • Geodesic flow
  • Hyperbolic geodesic
  • Nonlinearly stable
  • Prime-end compactification
  • Transverse homoclinic intersections

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Xia, Z., & Zhang, P. (2017). Homoclinic intersections for geodesic flows on convex spheres. In Contemporary Mathematics (pp. 221-238). (Contemporary Mathematics; Vol. 698). American Mathematical Society. https://doi.org/10.1090/conm/698/13980